Constellation rearrangement for transmit diversity schemes

ABSTRACT

A method of transmitting data in a wireless communication system from a transmitter to a receiver, comprising the steps of modulating data at the transmitter using a first signal constellation pattern to obtain a first data symbol. The first data symbol is transmitted to the receiver using a first diversity branch. Further, the data is modulated at the transmitter using a second signal constellation pattern to obtain a second data symbol. Then, the second data symbol is transmitted to the receiver over a second diversity path. Finally, the received first and second data symbol are diversity combined at the receiver. 
     The invention further relates to a transmitter and a receiver embodied to carry out the method of the invention.

This is a continuation application of application Ser. No. 12/484,060 filed Jun. 12, 2009, which is a continuation application of application Ser. No. 11/634,127 filed Dec. 6, 2006, which is a continuation application of application Ser. No. 10/501,905 filed Jul. 20, 2004, which is a national stage of PCT/EP2002/011695 filed Oct. 18, 2002, the entire contents of each which are incorporated by reference herein.

The present invention relates generally to transmission techniques in wireless communication systems and in particular to a method, transceiver and receiver using transmit diversity schemes wherein the bit-to-symbol mapping is performed differently for different transmitted diversity branches. The invention is particularly applicable to systems with unreliable and time-varying channel conditions resulting in an improved performance avoiding transmission errors.

There exist several well known transmit diversity techniques wherein one or several redundancy versions relating to identical data are transmitted on several (at least two) diversity branches “by default” without explicitly requesting (by a feedback channel) further diversity branches (as done in an ARQ scheme by requesting retransmissions). For example the following schemes are considered as transmit diversity:

-   -   Site Diversity: The transmitted signal originates from different         sites, e.g. different base stations in a cellular environment.     -   Antenna Diversity: The transmitted signal originates from         different antennas, e.g. different antennas of a multi-antenna         base station.     -   Polarization Diversity: The transmitted signal is mapped onto         different polarizations.     -   Frequency Diversity: The transmitted signal is mapped e.g. on         different carrier frequencies or on different frequency hopping         sequences.     -   Time Diversity: The transmitted signal is e.g. mapped on         different interleaving sequences.     -   Multicode Diversity: The transmitted signal is mapped on         different codes in e.g. a CDMA (Code Division Multiple Access)         system.

There are known several diversity combining techniques. The following three techniques are the most common ones:

-   -   Selection Combining: Selecting the diversity branch with the         highest SNR for decoding, ignoring the remaining ones.     -   Equal Gain Combining: Combining received diversity branches with         ignoring the differences in received SNR.     -   Maximal Ratio Combining: Combining received diversity branches         taking the received SNR of each diversity branch into account.         The combining can be performed at bit-level (e.g. LLR) or at         modulation symbol level.

Furthermore, a common technique for error detection/correction is based on Automatic Repeat reQuest (ARQ) schemes together with Forward Error Correction (FEC), called hybrid ARQ (HARQ). If an error is detected within a packet by the Cyclic Redundancy Check (CRC), the receiver requests the transmitter to send additional information (retransmission) to improve the probability to correctly decode the erroneous packet.

In WO-02/067491 A1 a method for hybrid ARQ transmissions has been disclosed which averages the bit reliabilities over successively requested retransmissions by means of signal constellation rearrangement.

As shown therein, when employing higher order modulation formats (e.g. M-PSK, M-QAM with log₂(M)>2), where more than 2 bits are mapped onto one modulation symbol, the bits mapped onto a modulation symbol have different reliabilities depending on their content and depending on the chosen mapping. This leads for most FEC (e.g. Turbo Codes) schemes to a degraded decoder performance compared to an input of more equally distributed bit reliabilities.

In conventional communication systems the modulation dependent variations in bit reliabilities are not taken into account and, hence, usually the variations remain after combining the diversity branches at the receiver.

The object of the invention is to provide a method, transmitter and receiver which show an improved performance with regard to transmission errors. This object is solved by a method, transmitter and receiver as set forth in the independent claims.

The invention is based on the idea to improve the decoding performance at the receiver by applying different signal constellation mappings to the available distinguishable transmit diversity branches. The idea is applicable to modulation formats, where more than 2 bits are mapped onto one modulation symbol, since this implies a variation in reliabilities for the bits mapped onto the signal constellation (e.g. for regular BPSK and QPSK modulation all bits mapped onto a modulation symbol have the same reliability). The variations depend on the employed mapping and on the actually transmitted content of the bits.

Depending on the employed modulation format and the actual number of bits mapped onto a single modulation symbol, for a given arbitrary number (N>1) of available diversity branches the quality of the averaging process is different. Averaging in the sense of the present invention is understood as a process of reducing the differences in mean combined bit reliabilities among the different bits of a data symbol. Although it might be that only after using several diversity branches or paths a perfect averaging with no remaining differences is achieved, averaging means in the context of the document any process steps in the direction of reducing the mean combined bit reliability differences. Assuming on average an equal SNR for all available diversity branches, for 16-QAM 4 mappings (4 diversity branches) would be needed to perfectly average out the reliabilities for all bits mapped on any symbol. However, if e.g. only 2 branches are available a perfect averaging is not possible. Hence, the averaging should then be performed on a best effort basis as shown in the example below.

The present invention will be more readily understood from the following detailed description of preferred embodiments with reference to the accompanying figures which show:

FIG. 1 an example for a 16-QAM signal constellation;

FIG. 2 an example for a different mapping of a 16-QAM signal constellation;

FIG. 3 two further examples of 16-QAM signal constellations;

FIG. 4 an exemplary embodiment of a communication system according to the present invention; and

FIG. 5 details of a table for storing a plurality of signal constellation patterns.

The following detailed description is shown for a square 16-QAM with Gray mapping. However, without loss of generality the shown example is extendable to other M-QAM and M-PSK (with log₂(M)>2) formats. Moreover, the examples are shown for transmit diversity schemes transmitting an identical bit-sequence on both branches (single redundancy version scheme). Then again, an extension to a transmit diversity scheme transmitting only partly identical bits on the diversity branches can be accomplished. An example for a system using multiple redundancy versions is described in copending EP 01127244, filed on Nov. 16, 2001. Assuming a turbo encoder, the systematic bits can be averaged on a higher level as compared to the parity bits.

Assuming a transmit diversity scheme with two generated diversity branches, which are distinguishable at the receiver (e.g. by different spreading or scrambling codes in a CDMA system, or other techniques of creating orthogonal branches) and a transmission of the same redundancy version, usually the received diversity branches are combined at the receiver before applying the FEC decoder. A common combining technique is the maximal ratio combining, which can be achieved by adding the calculated log-likelihood-ratios LLRs from each individual received diversity branch.

The log-likelihood-ratio LLR as a soft-metric for the reliability of a demodulated bit b from a received modulation symbol r=x+jy is defined as follows:

$\begin{matrix} {{{LLR}(b)} = {\ln \left\lbrack \frac{\Pr \left\{ {b = \left. 1 \middle| r \right.} \right\}}{\Pr \left\{ {b = \left. 0 \middle| r \right.} \right\}} \right\rbrack}} & (1) \end{matrix}$

As can be seen from FIG. 1 (bars indicate rows/columns for which the respective bit equals 1), the mappings of the in-phase component bits and the quadrature component bits on the signal constellation are orthogonal (for M-PSK the LLR calculation cannot be simplified by separating into complex components, however the general procedure of bit-reliability averaging is similar). Therefore, it is sufficient to focus on the in-phase component bits i₁ and i₂. The same conclusions apply then for q₁ and q₂.

Assuming that Mapping 1 from FIG. 1 is applied for the bit-to-symbol mapping for the 1^(st) diversity branch, the log-likelihood-ratio LLR of the most significant bit (MSB) i₁ and the least significant bit (LSB) i₂ yields the following equations for a Gaussian channel:

$\begin{matrix} {{{LLR}\left( i_{1} \right)} = {\ln \left\lbrack \frac{^{- {K{({x + x_{0}})}}^{2}} + ^{- {K{({x + x_{1}})}}^{2}}}{^{- {K{({x - x_{0}})}}^{2}} + ^{- {K{({x - x_{1}})}}^{2}}} \right\rbrack}} & (2) \\ {{{LLR}\left( i_{2} \right)} = {\ln \left\lbrack \frac{^{- {K{({x + x_{1}})}}^{2}} + ^{- {K{({x + x_{1}})}}^{2}}}{^{- {K{({x - x_{0}})}}^{2}} + ^{- {K{({x + x_{0}})}}^{2}}} \right\rbrack}} & (3) \end{matrix}$

where x denotes the in-phase component of the normalized received modulation symbol r and K is a factor proportional to the signal-to-noise ratio. Under the assumption of a uniform signal constellation (x₁=3x₀,regular 16-QAM) equations (2) and (3) can be fairly good approximated as shown in S. Le Goff, A. Glavieux, C. Berrou, “Turbo-Codes and High Spectral Efficiency Modulation,” IEEE SUPERCOMM/ICC '94, Vol. 2, pp. 645-649, 1994, and Ch. Wengerter, A. Golitschek Eder von Elbwart, E. Seidel, G. Velev, M. P. Schmitt, “Advanced Hybrid ARQ Technique Employing a Signal Constellation Rearrangement,” IEEE Proceedings of VTC 2002 Fall, Vancouver, Canada, September 2002 by

LLR(i ₁)≈−4Kx ₀ x  (4)

LLR(i ₂)≈−4Kx ₀(2x ₀ ˜|x|)  (5)

The mean LLR for i₁ and i₂ for a given transmitted modulation symbol yields the values given in Table 1 (substituting 4Kx₀ ² by Λ). Mean in this sense, refers to that the mean received value for a given transmitted constellation point, exactly matches this transmitted constellation point. Individual samples of course experience noise according to the parameter K. However, for a Gaussian channel the mean value of the noise process is zero. In case of transmitted modulation symbols 0 q ₁ 1 q ₂ and 1 q ₁ 1 q ₂, where q₁ and q₂ are arbitrary, the magnitude of the mean LLR (i₁) is higher than of the mean LLR (i₂). This means that the LLR for the MSB i₁ depends on the content of the LSB i₂; e.g. in FIG. 1 i₁ has a higher mean reliability in case the logical value for i₂ equals 1 (leftmost and rightmost columns). Hence, assuming a uniform distribution of transmitted modulation symbols, on average 50% of the MSBs i₁ have about three times the magnitude in LLR of i₂.

TABLE 1 Mean LLRs for bits mapped on the in-phase component of the signal constellation for Mapping 1 in FIG. 1 according to equations (4) and (5). Symbol Mean value (i₁q₁i₂q₂) of x Mean LLR (i₁) Mean LLR (i₂) 0q₁0q₂  x₀ −4Kx₀ ² = −Λ −4Kx₀ ² = −Λ 0q₁1q₂  x₁ −12Kx₀ ² = −3Λ 4Kx₀ ² = Λ 1q₁0q₂ −x₀ 4Kx₀ ² = Λ −4Kx₀ ² = −Λ 1q₁1q₂ −x₁ 12Kx₀ ² = 3Λ 4Kx₀ ² = Λ

If now adding a 2^(nd) transmit diversity branch transmitting e.g. an identical bit sequence prior art schemes would employ an identical mapping to the 1^(st) diversity branch. Here, it is proposed to employ a 2^(nd) signal constellation mapping (Mapping 2) according to FIG. 2 (of course, also one of the constellations depicted in FIG. 3 are possible), which yields the mean LLRs given in Table 2.

TABLE 2 Mean LLRs for bits mapped on the in-phase component of the signal constellation for Mapping 2 in FIG. 2. Symbol Mean value (i₁q₁i₂q₂) of x Mean LLR (i₁) Mean LLR (i₂) 0q₁0q₂  x₀ −Λ −3Λ 0q₁1q₂  x₁ −Λ  3Λ 1q₁0q₂ −x₀  Λ  −Λ 1q₁1q₂ −x₁  Λ  Λ

Comparing now the soft-combined LLRs of the received diversity branches applying the constellation rearrangement (Mapping 1+2) and applying the identical mappings (Mapping 1+1, prior art), it can be observed from table 3 that the combined mean LLR values with applying the constellation rearrangement have a more uniform distribution (Magnitudes: 4×4Λ and 4×2Λ instead of 2×6Λ and 6×2Λ). For most FEC decoders (e.g. Turbo Codes and Convolutional Codes) this leads to a better decoding performance. Investigations have revealed that in particular Turbo encoding/decoding systems exhibit a superior performance. It should be noted, that the chosen mappings are non exhaustive and more combinations of mappings fulfilling the same requirements can be found.

TABLE 3 Mean LLRs (per branch) and combined mean LLRs for bits mapped on the in-phase component of the signal constellation for the diversity branches when employing Mapping 1 and 2 and when employing 2 times Mapping 1. Constellation Prior Art Rearrangement No Rearrangement Transmit (Mapping 1 + 2) (Mapping 1 + 1) Diversity Symbol Mean Mean Mean Mean Branch (i₁q₁i₂q₂) LLR (i₁) LLR (i₂) LLR (i₁) LLR (i₂) 1 0q₁0q₂  −Λ  −Λ  −Λ −Λ 0q₁1q₂ −3Λ  Λ −3Λ  Λ 1q₁0q₂  Λ  −Λ  Λ −Λ 1q₁1q₂  3Λ  Λ  3Λ  Λ 2 0q₁0q₂  −Λ −3Λ  −Λ −Λ 0q₁1q₂  −Λ  3Λ −3Λ  Λ 1q₁0q₂  Λ  −Λ  Λ −Λ 1q₁1q₂  Λ  Λ  3Λ  Λ Combined 0q₁0q₂ −2Λ −4Λ −2Λ −2Λ  1 + 2 0q₁1q₂ −4Λ −4Λ −6Λ 2Λ 1q₁0q₂  2Λ −2Λ  2Λ −2Λ  1q₁1q₂  4Λ  2Λ  6Λ 2Λ

In the following an example with 4 diversity branches will be described. Here, the same principles apply as for 2 diversity branches. However, since 4 diversity branches are available and the averaging with 2 diversity branches is not perfect, additional mappings can be used to improve the averaging process.

FIG. 3 shows the additional mappings for diversity branches 3 and 4, under the assumption that Mappings 1 and 2 are used for branches 1 and 2 (in FIG. 1 and FIG. 2). Then the averaging can be performed perfectly and all bits mapped on any symbol will have an equal mean bit reliability (assuming the same SNR for all transmissions). Table 4 compares the LLRs with and without applying the proposed Constellation Rearrangement. Having a closer look at the combined LLRs, it can be seen that with application of the Constellation Rearrangement the magnitude for all bit reliabilities results in 6Λ.

It should be noted again, that the chosen mappings are non exhaustive and more combinations of mappings fulfilling the same requirements can be found.

TABLE 4 Mean LLRs (per branch) and combined mean LLRs for bits mapped on the in-phase component of the signal constellation for the diversity branches when employing Mappings 1 to 4 and when employing 4 times Mapping 1. Constellation Prior Art Rearrangement No Rearrangement (Mapping 1 + 2 + (Mapping 1 + 1 + Transmit 3 + 4) 1 + 1) Diversity Symbol Mean Mean Mean Mean Branch (i₁q₁i₂q₂) LLR (i₁) LLR (i₂) LLR (i₁) LLR (i₂) 1 0q₁0q₂ −Λ −Λ  −Λ −Λ 0q₁1q₂ −3Λ   Λ −3Λ  Λ 1q₁0q₂  Λ −Λ  Λ −Λ 1q₁1q₂ 3Λ  Λ  3Λ  Λ 2 0q₁0q₂ −Λ −3Λ   −Λ −Λ 0q₁1q₂ −Λ 3Λ −3Λ  Λ 1q₁0q₂  Λ −Λ  Λ −Λ 1q₁1q₂  Λ  Λ  3Λ  Λ 3 0q₁0q₂ −Λ −Λ  −Λ −Λ 0q₁1q₂ −Λ  Λ −3Λ  Λ 1q₁0q₂  Λ −3Λ   Λ −Λ 1q₁1q₂  Λ 3Λ  3Λ  Λ 4 0q₁0q₂ −3Λ  −Λ  −Λ −Λ 0q₁1q₂ −Λ  Λ −3Λ  Λ 1q₁0q₂ 3Λ −Λ  Λ −Λ 1q₁1q₂  Λ  Λ  3Λ  Λ Combined 0q₁0q₂ −6Λ  −6Λ  −4Λ −4Λ  1 + 2 + 0q₁1q₂ −6Λ  6Λ −12Λ  4Λ 3 + 4 1q₁0q₂ 6Λ −6Λ   4Λ −4Λ  1q₁1q₂ 6Λ 6Λ 12Λ 4Λ

If the constellation rearrangement is performed by applying different mapping schemes, one would end up in employing a number of different mappings as given in FIG. 1, FIG. 2 and FIG. 3. If the identical mapper (e.g. FIG. 1) should be kept for all transmit diversity branches, e.g. mapping 2 can be obtained from mapping 1 by the following operations:

-   -   exchange positions of original bits i₁ and i₂ exchange positions         of original bits q₁ and q₂     -   logical bit inversion of original bits i₁ and q₁

Alternatively, those bits that end in positions 1 and 2 can also be inverted (resulting in a different mapping with an identical bit-reliability characteristics).

Therefore, the following table provides an example how to obtain mappings 1 to 4 (or mappings with equivalent bit reliabilities for i₁, i₂, q₁ and q₂), where the bits always refer to the first transmission, and a long dash above a character denotes logical bit inversion of that bit:

TABLE 5 Alternative implementation of the Constellation Rearrangement by interleaving (intra-symbol interleaving) and logical inversion of bits mapped onto the modulation symbols. Interleaver and Inverter Mapping No. functionality 1 i₁q₁i₂q₂ 2 ī₂ q ₂ī₁ q ₁ or i₂q₂ī₁ q ₁ 3 ī₂ q ₂i₁q₁ or i₂q₂i₁q₁ 4 i₁q₁i₂ q ₂ or ī₁ q ₁ī₂ q ₂

Generally at least 2 different mappings should be employed for N>9 diversity branches, where the order and the selection of the mappings is irrelevant, as long as the bit-reliability averaging process, meaning the (reduction of differences in reliabilities) is maintained.

Preferred realizations in terms of number of employed mappings

-   -   M-QAM         -   Employing log₂(M) different mappings         -   Employing log₂(M)/2 different mappings     -   M-PSK         -   Employing log₂(M) different mappings         -   Employing log₂(M)/2 different mappings         -   Employing 2log₂(M) different mappings

The applied signal constellation mappings for modulation at the transmitter and demodulation at the receiver need to match for each individual transmit diversity branch. This can be achieved by appropriate signalling of parameters indicating the proper mapping or combination of mappings to be applied for the diversity branches. Alternatively the definition of the mappings to be applied for transmit diversity branches may be system predefined.

FIG. 4 shows an exemplary embodiment of a communication system according to the present invention. More specifically, the communication system comprises a transmitter 10 and a receiver 20 which communicate through a communication channel consisting of a plurality of diversity branches 40A, 40B and 40C. Although three diversity branches are illustrated in the figure, it becomes clear to a person skilled in the art that an arbitrary number of branches may be chosen. From a data source 11, data packets are supplied to a FEC encoder 12, preferably a FEC Turbo encoder, where redundancy bits are added to correct errors. The bits output from the FEC encoder are subsequently supplied to a mapping unit 13 acting as a modulator to output symbols formed according to the applied modulation scheme stored as a constellation pattern in a table 15. Subsequently the data symbols are applied to a transmission unit 30 for transmission over the branches 40A-C. The receiver 20 receives the data packets by the receiving unit 35. The bits are then input into a demapping unit 21 which acts as a demodulator using the same signal constellation pattern stored in the table 15 which was used during the modulation of that symbol.

The demodulated data packets received over one diversity branch are stored in a temporary buffer 22 for subsequent combining in a combining unit 23 with the data packets received over at least one other diversity branch.

As illustrated in FIG. 5, table 15 stores a plurality of signal constellation patterns #0 . . . #n which are selected for the individual transmissions over the individual diversity branches according to a predetermined scheme. The scheme, i.e. the sequence of signal constellation patterns used for modulating/demodulating are either pre-stored in the transmitter and the receiver or are signalled by transmitter to the receiver prior to usage. 

1. A method of transmitting data comprising: mapping first bits of the data applying a first mapping rule or a 16-QAM modulation scheme; mapping second bits of the data applying a second mapping rule or the 16-QAM modulation scheme, the second bits being different from the first bits; and transmitting the mapped first bits of the data and the second bits of the data to a receiver in a first branch and a second branch.
 2. The method according to claim 1, wherein the branch is a site, a base station, an antenna, a polarized wave, a frequency, a time, or a code.
 3. The method according to claim 1, wherein a mapper used in the second mapping rule is the same as a mapper used in the first mapping rule.
 4. The method according to claim 1, wherein the second bits are obtained by interleaving the positions of the first bits with a logical bit inversion.
 5. The method according to claim 1, wherein the first and second mapping rules are selected such that after a combining the bits of the data, the differences in bit reliabilities among the different bit arrangements of one data symbol are reduced.
 6. A transmitter for transmitting data comprising: a first modulation section that maps first bits of the data applying a first mapping rule or a 16-QAM modulation scheme; a second modulation section that maps second bits of the data applying a second mapping rule or the 16-QAM modulation scheme, the second bits being different from the first bits, and a transmission section that transmits the mapped first bits of the data and the mapped second bits of the data to a receiver in a first branch and a second branch.
 7. The transmitter according to claim 6, wherein the branch is a site, a base station, an antenna, a polarized wave, a frequency, a time, or a code.
 8. The transmitter according to claim 6, wherein a mapper used in the second mapping rule is the same as a mapper used in the first mapping rule.
 9. The transmitter according to claim 6, wherein the second bits are obtained by interleaving the positions of the first bits with a logical bit inversion.
 10. The transmitter according to claim 6, wherein the first and second mapping rules are selected such that after a combining the bits of the data, the differences in bit reliabilities among the different bit arrangements of one data symbol are reduced.
 11. A method of receiving data comprising: receiving first bits of the data and second bits of the data from a transmitter in a first branch and a second branch; de-mapping the received first and second bits of the data at the receiver applying a first mapping rule or a 16-QAM modulation scheme and a second mapping rule or the 16-QAM modulation scheme, the second bits being different from the first bits; and combining the de-mapped first and second bits of the data.
 12. A receiver for receiving data comprising: a reception section that receives first bits of the data and second bits of the data from a transmitter in a first branch and a second branch; a demodulation section that de-maps the received first and second bits of the data applying a first mapping rule or a 16-QAM modulation scheme and a second mapping rule or the 16-QAM modulation scheme, the second bits being different from the first bits; and a combination section that combines the de-mapped first and second bits of the data. 